PROVE TO ME THAT YOU'RE DIVINE ...CHANGE MY WATER INTO WINE!
This is known as the DIOPHANTINE equation .. a CONJECTURE known for thousands of years .. . Fermat a GREAT ,GREAT FRENCH mathematician . anounced that he had A PROOF . Unfurtunatly the proof got lost .. And it took 300 more years to be proved .. The proof is a TECHNOLOGICAL TOUR DE FORCE .. It envolves transformations of the form of the equation and manipulations in recent mathamatics ... Is a not a beautiful proof, NOT elegant , But probably a starting point to go back to NUMBER THEORY and try to find an equivalent proof there!
look for the NOTES on FERMAT'S last THEOREM by A.J. VAN DER POORTEN Macquarie UNIVERSITY .